Identification of Hydrodynamic Dispersion Tensor by Optimization Algorithm Based LBM/CMA-ES Combination
The hydrodynamic dispersion tensor (HDT) of a porous medium is a key parameter in engineering and environmental sciences. Its knowledge allows for example, to accurately predict the propagation of a pollution front induced by a surface (or subsurface) flow. This paper proposes a new mathematical mod...
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MDPI AG
2022-01-01
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| author | Hassan Smaoui Lahcen Zouhri Sami Kaidi |
| author_facet | Hassan Smaoui Lahcen Zouhri Sami Kaidi |
| author_sort | Hassan Smaoui |
| collection | DOAJ |
| description | The hydrodynamic dispersion tensor (HDT) of a porous medium is a key parameter in engineering and environmental sciences. Its knowledge allows for example, to accurately predict the propagation of a pollution front induced by a surface (or subsurface) flow. This paper proposes a new mathematical model based on inverse problem-solving techniques to identify the HDT (noted <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mi mathvariant="bold-italic">D</mi><mo>=</mo></mover></mrow></semantics></math></inline-formula>) of the studied porous medium. We then showed that in practice, this new model can be written in the form of an integrated optimization algorithm (IOA). The IOA is based on the numerical solution of the direct problem (which solves the convection–diffusion type transport equation) and the optimization of the error function between the simulated concentration field and that observed at the application site. The partial differential equations of the direct model were solved by high resolution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mo>Δ</mo><mi>x</mi><mo>=</mo><mo>Δ</mo><mi>y</mi><mo>=</mo><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> Lattice Boltzmann Method (LBM) whose computational code is named HYDRODISP-LBM (HYDRO-DISpersion by LBM). As for the optimization step, we opted for the CMA-ES (Covariance Matrix Adaptation-Evolution Strategy) algorithm. Our choice for these two methods was motivated by their excellent performance proven in the abundant literature. The paper describes in detail the operation of the coupling of the two computer codes forming the IOA that we have named HYDRODISP-LBM/CMA-ES. Finally, the IOA was applied at the Beauvais experimental site to identify the HDT <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mi mathvariant="bold-italic">D</mi><mo>=</mo></mover></mrow></semantics></math></inline-formula>. The geological analyzes of this site showed that the tensor identified by the IOA is in perfect agreement with the characteristics of the geological formation of the site which are connected with the mixing processes of the latter. |
| first_indexed | 2024-03-10T03:11:12Z |
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| spelling | doaj.art-267523180a5b4795975c4a7f5e5ef37a2023-11-23T12:33:17ZengMDPI AGWater2073-44412022-01-0114112510.3390/w14010125Identification of Hydrodynamic Dispersion Tensor by Optimization Algorithm Based LBM/CMA-ES CombinationHassan Smaoui0Lahcen Zouhri1Sami Kaidi2CEREMA Risques Eaux et Mer (REM) EPR HA, 134 Rue de Beauvais, 60280 Margny-Les-Compiègne, FranceAGHYLE, Institut Polytechnique UniLaSalle Beauvais, SFR Condorcet FR CNRS 3417 19 Rue Pierre Waguet, 60026 Beauvais, FranceCEREMA Risques Eaux et Mer (REM) EPR HA, 134 Rue de Beauvais, 60280 Margny-Les-Compiègne, FranceThe hydrodynamic dispersion tensor (HDT) of a porous medium is a key parameter in engineering and environmental sciences. Its knowledge allows for example, to accurately predict the propagation of a pollution front induced by a surface (or subsurface) flow. This paper proposes a new mathematical model based on inverse problem-solving techniques to identify the HDT (noted <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mi mathvariant="bold-italic">D</mi><mo>=</mo></mover></mrow></semantics></math></inline-formula>) of the studied porous medium. We then showed that in practice, this new model can be written in the form of an integrated optimization algorithm (IOA). The IOA is based on the numerical solution of the direct problem (which solves the convection–diffusion type transport equation) and the optimization of the error function between the simulated concentration field and that observed at the application site. The partial differential equations of the direct model were solved by high resolution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mo>Δ</mo><mi>x</mi><mo>=</mo><mo>Δ</mo><mi>y</mi><mo>=</mo><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> Lattice Boltzmann Method (LBM) whose computational code is named HYDRODISP-LBM (HYDRO-DISpersion by LBM). As for the optimization step, we opted for the CMA-ES (Covariance Matrix Adaptation-Evolution Strategy) algorithm. Our choice for these two methods was motivated by their excellent performance proven in the abundant literature. The paper describes in detail the operation of the coupling of the two computer codes forming the IOA that we have named HYDRODISP-LBM/CMA-ES. Finally, the IOA was applied at the Beauvais experimental site to identify the HDT <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mi mathvariant="bold-italic">D</mi><mo>=</mo></mover></mrow></semantics></math></inline-formula>. The geological analyzes of this site showed that the tensor identified by the IOA is in perfect agreement with the characteristics of the geological formation of the site which are connected with the mixing processes of the latter.https://www.mdpi.com/2073-4441/14/1/125groundwaternumerical modelinglattice Boltzmann methodrelaxation timehydrodynamicsisotropy |
| spellingShingle | Hassan Smaoui Lahcen Zouhri Sami Kaidi Identification of Hydrodynamic Dispersion Tensor by Optimization Algorithm Based LBM/CMA-ES Combination Water groundwater numerical modeling lattice Boltzmann method relaxation time hydrodynamics isotropy |
| title | Identification of Hydrodynamic Dispersion Tensor by Optimization Algorithm Based LBM/CMA-ES Combination |
| title_full | Identification of Hydrodynamic Dispersion Tensor by Optimization Algorithm Based LBM/CMA-ES Combination |
| title_fullStr | Identification of Hydrodynamic Dispersion Tensor by Optimization Algorithm Based LBM/CMA-ES Combination |
| title_full_unstemmed | Identification of Hydrodynamic Dispersion Tensor by Optimization Algorithm Based LBM/CMA-ES Combination |
| title_short | Identification of Hydrodynamic Dispersion Tensor by Optimization Algorithm Based LBM/CMA-ES Combination |
| title_sort | identification of hydrodynamic dispersion tensor by optimization algorithm based lbm cma es combination |
| topic | groundwater numerical modeling lattice Boltzmann method relaxation time hydrodynamics isotropy |
| url | https://www.mdpi.com/2073-4441/14/1/125 |
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